April doesn't wear the false eyelashes with Melanie because she feels comfortable and accepted by her new friend, and is not afraid to be herself.
April has had a difficult childhood. She has changed schools a lot, and her mother is irresposible and repeatedly abandons her. To keep herself from feeling the pain of constant rejection, April puts on a facade, hiding behind her fake eyelashes and affected mannerisms, and acting like she is better than everyone else and doesn't care if they don't like her. What April really wants so desperately is to be accepted and loved, but she has learned that those things do not come easily in her life. Her false eyelashes are a defense mechanism, something she can hide behind to keep from being hurt.
As September approaches, April becomes worried about starting school. She knows "from experience - lots of it - that it isn't easy to face a new class in a new school." April plans to wear her fake eyelashes to school to help innure her from the rejection she is sure will come, but Melanie perceptively advises against it. Melanie sees what April does not, that the eyelashes will make her adjustment even more difficult. Melanie has gotten to know April and likes her a lot; she knows that April's best chance of being accepted in her new school is for her to drop her affectations and just be herself (Chapter 4 -"The Egypt Girls").